Lucy07,
Welcome to cruise chat. Princess and HAL are excellent choices for the Alaska Cruise/tour. They have been doing Alaska longer than any of the other cruise lines. I must say though that any of the cruise lines sailing Alaska do a good job. Including Carnival. The party image of Carnival is an antiquated image they have been shedding for years.
Alaska Cruise tours can be very complicated and have many different combinations. I would highly recommend you find a cruise oriented travel agent and sit down and discuss what you are looking for in your Alaska vacation. They can help you sort out all the numerous combinations of the cruise tour.